Question: $A$ $B$ $C$ If: $ AC = 175$, $ AB = 9x + 8$, and $ BC = 9x + 5$, Find $BC$.
Solution: From the diagram, we can see that the total length of ${AC}$ is the sum of ${AB}$ and ${BC}$ $ {AB} + {BC} = {AC}$ Substitute in the expressions that were given for each length: $ {9x + 8} + {9x + 5} = {175}$ Combine like terms: $ 18x + 13 = {175}$ Subtract $13$ from both sides: $ 18x = 162$ Divide both sides by $18$ to find $x$ $ x = 9$ Substitute $9$ for $x$ in the expression that was given for $BC$ $ BC = 9({9}) + 5$ Simplify: $ {BC = 81 + 5}$ Simplify to find ${BC}$ : $ {BC = 86}$